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I wanted to start a discussion on this topic of thinking about the intraday high to low range of the S&P futures and the level of the VIX. I am not an options expert by any means -- but have spoken to some option market makers about this and here are some thoughts. Any options experts that would like to chime in would be great for discussion.

1. VIX and range should be related

VIX is 30-day implied volatility of returns. The term 'returns' implies that it is measuring the 'closing price to closing price' volatility. So there is a difference here -- 'close to close' is different than 'range' (ie, the high vs the low). Nevertheless, the ranges will likely be affected by the same things that are causing 'close-to-close return volatility'.

2. VIX Math Basics: VIX is stated as an annual percentage

To convert an annual VIX percentage to a single day percentage, the math is to take the square root of the number of trading days in a year. ie 252^(1/2). Divide VIX by this number (~15.9).

example, a 30 VIX equates to a single day return volatility of 30 / (252^0.5)

=~1.89%

This would be the expected average daily % change over the next 30 days.

You can re-arrange this formula and ballpark an implied volatility from daily returns. For example, if price has varied by 1.89% -- then you have"

(252^0.5) = ~15.9

.0189 x 15.9 = 30

Note, VIX is a weighted average of the current month and next month options volatility. This calculation is done every day such that you are always comparing apples to apples (ie, if you used only the near-term contract then it wouldn't be a consistent 30-day-forward looking calculation).

3. How does VIX do at predicting the forward 30-day close-to-close return volatility?

I am not going to go into this as this is a lengthy discussion for which I am not fully qualified. But basically, it does a fair job.

4. How does VIX do at predicting the NEXT DAYS range?

I am not going to present all the data here but here are some highlights:

over the last 7 years:

the S&P futures have achieved the implied range of the previous days closing VIX 54% of the time. In 2008, a year of ever rising VIX, this figure was 65%. The lowest year was 2007 at 42%.

Now, let me be clear that this is just a 'thought piece' and not supposed to be used for hard and fast rules. A few ideas:

Expect the market to do a range that falls between 0.7 and 1.3x what VIX is implying much of the time.

About 5% of the time, the range has been > 2.0x what VIX implied (these are the outliers).

About 30% of time, market will do 1.4x or more what VIX implied for a range.

(these numbers are based on historical 7 years and should not be thought of as precise forecasts of the future).

I have done some quick EasyLanguage code to present a working idea for an indicator for using this concept (note you input the previous days closing VIX -- or some estimate of what you think is the 'right' forward VIX estimate is --- and it spits out the projections to track against the developing high-to-low range):

EL Code:

inputs: VIX(46);

value1=squareroot(252);

value2=(VIX/100)/value1;

value3=closed(1)*(value2*1.0);

value4=highd(0)-lowd(0);

value10=closed(1)*(value2*1.0);

value11=closed(1)*(value2*0.7);

value12=closed(1)*(value2*1.3);

if time > 934 then

Plot1(value4,"+Range");

if time > 934 then

Plot2(value10,"1.0");

if time > 934 then

Plot3(value11,"0.7");

if time > 934 then

Plot4(value12,"1.3");

Edited by Frank

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Review for today:

After the large 46pt range from tuesday was followed by low range on Feb 11, was expecting a better high to low range today and we got that.

I saw 45 VIX and thought this might mean 20-30 pts of range. Final range was 31.25 pts.

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Recent Data:

The ratio listed represents the relationship between the actual range relative to the projection based on the previous closing VIX.

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Did some more work on this topic.

As previously stated, the VIX is essentially a forecast by market participants about the near-term return volatility. But as I look at the data for the past 7 years, you can see the relationship in the red bars below.

Red bars are calculated as follows.

Project the close to close volatility (absolute return) based on the previous days close and closing VIX. Then take the actual return and create a ratio of actual vs implied. Do this every day over past 7 years and show: on how many days does it close where VIX implied (absolute so either up or down). This is a frequency distribution --- so what this implies is that the market has lots of 'recovery' days back towards previous days close --- (since median ratio is much less than 1.0). Thus, it also implies that despite the many recovery days that only get 1/2 as far as VIX would imply, you get a small number of LARGE moves that go more than VIX implies. You won't see this in a frequency distribution because frequency is not going to calculate that. Frequency is good for intraday traders because you don't care so much about the outliers (if you are just short-term trading and you use stops). You care more about taking pieces out of the market on all those days where it does what the odds say it will do.

I like to think about this like an options trader might. An options trader gets a premium to take 'fat tail' risk. So, once the market has done its range (the move away from previous days close), you can think of it as an options trader selling options premium at inflated prices and playing for the recovery (as it does on majority of days). The problem for option traders comes when you get those small number of days with very large moves -- then the options go in the money and trader loses all those accumulated profits.

The way to think about this conceptually is -- figure out your directional bias -- but be wary of late reversals back towards the previous days close once the market gets extended. ie, expect the 'range' to get hit and don't be afraid to go for big win when all lines up --- but at some point, get out -- odds are that on many days, your gains will evaporate if you attempt to hold on until the close.

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Hi frank nice observations.

I am an option writer, but I trade in Indian markets not much in s & p ..but option market is somewhat same. I use VIX and OI PCR( open interest put call ratio ) in my trades. what I do is, i divide open interest put call ratio by VIX which gives directional bias of the underlying price moves, rising vix is indirectly proportional to price movements in this case s&p500 and oi pcr is directly proportional to price moves.

OIPCR rises when there is comparatively higher put writing than call writing, very few times vix rises and oipcr rises, then net change of vix/oipcr is almost zero and so filter out the noise without getting delay, but most of the time there is more put writing happens when vix is falling and so oipcr rises, on rising vix there is comparatively more call writing happens indicating weakness in markets, and for option writer, writing call option is safer bet than writing put option as probability model skewed towards fall, speed of fall is more than speed of rise in prices…

Hope to get other interesting ideas on vix from other known members and pardon me for such a long post.

Alex

Edited by alex_laxya

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alex, can you post a chart or two of that?

also, how do you time this indicator into a trade?

thanks for the interesting post.

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alex, can you post a chart or two of that?

also, how do you time this indicator into a trade?

thanks for the interesting post.

It was just sample chart, not my trade setup, in first window is nifty, NIFTY is same as s&p500, most liquid index derivative contract, in second window its vix ( mathematical formula of nsevix is same as cboe vix ) in third window is oipcr

By arrow i suggested the practical use to get directional sense.

While there r other things as well, instead of depending completely on it i try to put this data in overall context and also there r few things like oipcr has historical resistance at 169-1.75 zone ( in this one year old so called bear cycle )also need of smoothing the data to reduce the noise without getting delay response etc..to make a more reliable and logical combination, more i posted here

scroll down to post 29,later half of the section, posted the chart over there for trading setup.

vix_comp_meth.pdf

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today a good example of what 'fits' the general concept I was trying to relay. The market traded a wide range and recovered late towards the previous days close.

Using a VIX of 50 and Thursdays Closing Price of 686.50, a 'normal' day would be a range of 21.5 points and a close back towards the previous days close off the afternoon high or low. Conceptually, this is what happened as from an option traders view, you got paid to sell puts after doing a lot of range.

686.50 Previous Days Close

688.50 Final Close

+ 2pts Final Change after trading as low as 665.75 (Low of Day)

Edited by Frank

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So let's put some hard statistics to work within this VIX implied framework - this data is for the past 7 years and includes 1780 days in the sample:

1) Expect the Final RANGE for the day (pit-session only) to get at least >0.8x what VIX implies. If You expect this for all days, you will be right about 80% of time (this stat might be more powerful than as stated given a decent % of the days that fall short are affected by days such as 'day before FOMC meeting', day before holiday etc...)

2) Expect the market to CLOSE less than 1.2x the VIX implied move >80% of time. That is, the closing price vs previous close will have a bit of gravity aspect to it.

Summary: The above are guidelines and somewhat at odds with each other. On the one hand, you expect a MINIMUM range and would not be 'surprised' if range extended to 1.4x the implied range (that implied by VIX). On the other hand, and close that goes much more than 1.2x the implied move of VIX and you start to enter 'outlier status'.

Let me state again that frequency distributions are good for short-term traders -- as you are playing a tendency that occurs MOST of the time. The key is to find ways to trade WITH the statistical tendencies -- but implement risk-controlled strategies that allow you to participate in the statistical tendencies while not getting caught on the wrong side of the 'outliers.' This should be used as a mental framework only -- and certainly used in conjunction with other concepts in mind.

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Wanted to continue this thread as kind of a diary with periodic updates.

ok, coming into the day the pre-open projections were

Monday Closing VIX: 49

Monday ES Close: 675.50

VIX 1-Day Estimate = 3.09% = 0.49 / (252^0.5)

'Expected' Normal Range: 675.50 * 1-Day Estimate = 20.9 pts

Tuesday saw a gap up -- opening at 690.00

The early low was put in at 688.50 and price traded up hard

Now assuming a strong up day, an initial price projection for day would be 688.50 + 20.9 pts = ~709.50

Trading to that level would be consistent with a 'median' expectation.

Price will auction higher than that 50% of days so you need to make a judgment how strong the price action is. Today saw very strong price action, an 'adjusted' estimate could therefore be made to something higher and be consistent with the strong move up. turns out that 10% of days do see 1.8 or better type of range. (7 year data 2002-2009). You could therefore try to rationalize up to maybe 1.8x 21 pts = 37+ pts. off the early low of 688.50, that works out to 726.

But let's think about this from the close to close perspective for a cross-check. The distribution of closes vs previous days close vs VIX is skewed. The properties are less predictable given this skew. For this reason, let's use the intraday as primary source for price projections, and only use close to close projections as a 'sanity check'.

We know that 80% of days close < 1.2x VIX implies range from the previous close. But here we have a 'gap and go' day with extreme urgency of buyers (open-drive in Market Profile). You must respect the fact the the market is trending. Turns out that a 'top 10%' type of day from close to close is approximately 1.5x the VIX implied range.

So upside 'aggressive' projection using 1.5x is 20.9 x 1.5 = ~31.50 pts.

Using the previous close at 675.50 and 31.50 pts gets 707.00. Therefore, this sanity check argues that the initial 'intraday range' projection be made more conservative. Somewhere lower than 726 seems appropriate for 'upside case'. But 707 off an intraday low of 688.50 is < 20 pts ... in a market showing urgency, that is too low as our 'primary' projection tool is the intraday range. Perhaps a top quartile projection is 'reasonable'. Top quartile works out to 1.5x VIX implies = 31.35 pts.

What happened?

Final pit session range was 33.25 pts.

33.25 Pts works out to ~1.6x VIX implied intraday range

Close was 715.75 vs 675.50 previous close = +40.25 pts

40.25 pts / 20.9 VIX implied = 1.9x VIX implied close to close move.

These numbers are high -- but to some extent, they are completely consistent with the days action. Note how the market did slow down greatly once getting up towards 715. A bit of gravity took hold once got up into 'outlier' zone....

Where on the distributions does such action plot:

This analysis is just to show a framework for consideration.

Edited by Frank

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Wanted to talk about application of this concept.

The play today was long -- for reasons other than what this thread is about -- this thread is about relating VIX to intraday range. An application using this long assumption would be to 'stay long biased until XX points of range are achieved' -- and then stop trading and wait for the next day to create new odds-based price targets. Odds over the long run are that market does not close on one side of its range -- but it will do it sometimes. Better to get in, get your piece of the market and then get out.

For tomorrow:

VIX today closed ~44.

ES price close: 715.75

1-day base case median expectation:

When new information arrives tomorrow, adjustments to this baseline forecast will become appropriate.

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Elaborating on one thing today.

We know that the historical record shows that the relationship between the daily return and that implied by VIX is heavily 'skewed' (Positive Skew). That is, on a frequency basis -- strong majority of days will fall short of what VIX implies. That said, there will be some days that show strong urgency and trade hard away from the previous closing price -- causing the 'fat tail' -- and hurting those traders that do not adjust to this. Still, as day-traders, the odds are in your favor to fade a move away from the previous close on a day in, day out basis. You just better be ready to not get run over (and hopefully participate) in a strong trending move.

First chart is a text-book example of 'Positive Skew'

The Next Chart is The Actual Frequency Distribution From 2002 - 2009 which is calculated as a ratio of Actual Daily 'Close-to-Close' return.

Finally, for a case study. Here are the final results for the ES H9 contract which rolls tomorrow. (I did exclude a few of the christmas holiday days).

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todays journal entry takes a look at the condition that causes 'outliers'.

it was stated above that closing more than 1.1x the VIX implied range was the rarer case (has been less than 1 in 5 days over last 7 years -- not a 'outlier' -- but just the rarer case). for the H contract (including today), there were 12 instances that achieved the condition of closing more than 1.1x the VIX implied range (close vs previous day close divided by the 1-day vix projection). All 12 days had the same thing in common --- directional conviction off the first 30-min bar.

today for example, the low for the day was put in on the first 30-min bar and then price traded nothing but UP.

The attachment below shows all the days during the H contract (including today) that achieved the >1.1x 'unusual' close distinction. All days from the H contract were ranked by close vs previous close... the box in red shows the bar number (out of all 14 30-min bars) that the final low or high was made (choose low if day traded up, choose high if day traded down).

The idea here is to show the types of conditions that defines the 'directional conviction' that causes the outliers to the data set. we have one condition.

Edited by Frank

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Thanks for posting Frank, finding this interesting.

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Where todays statistics fall in context of the distribution. Classic consolidation day after a very big move yesterday. Today, slightly less movement than implied by VIX, but right in line with the fat parts of the respective distributions -- and in line with the thesis of this thread.

Edited by Frank

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todays journal entry is a video discussing this topic of range and using VIX to help decide direction for day and importantly, a way to think about price targets in relation to the odds presented in posts above:

copy paste these 2 url addresses together -- (some quirk with the traderslab site forces you to embed it within the thread otherwise):

/watch?v=DRouKY4qyco&fmt=18

Edited by Frank

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todays journal entry looks at the nature of time-series data.

Financial relationships are dynamic (they change over time). Short-term models are in a way better because they inherently have less 'error'. However, short-term models aren't stable because the less data you have, the less reliability and the less stability of the relationship under statistical investigation. So there is a trade-off.

The points is that when looking at time-series data, you must examine the extent to which the relationships are changing. If there is instability in a relationship, any regression that represents the relationship will be unstable.

There are statistical ways to deal with the problems presented by time-series data. However, I do not want to be too mathematical about this concept. Instead, I am just going to show the issues we face here.

Compare these two time periods from last year. Note how this relationship changed dramatically.

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The one 'rule' I take from the above charts is that whether in a declining or rising volatility environment, the S&P futures tend to exceed [~0.7 times the VIX implied range] the vast majority of the time. There seems to be a minimum range that can be counted upon. This is nice information to have when looking for conservative but reasonable price targets.

Here is current look (year to date):

Edited by Frank

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Today ranked 12th of last 20 days in terms of overall volatility (range), with range modestly higher than that which VIX implied. Classic 'Fat Distribution' Day where the closing price ends up near the previous close despite above average volatility. The change vs previous close ranked 19th of 20 in terms of movement at just ~0.1 vs VIX implied 1-day movement.

Edited by Frank

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Today, market made its low in opening 30-minutes and this led to the best move vs previous close in 13+ weeks:

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Just jumping in here not knowing if this has been said already but simply using the previous day or average of the previous 3 days range would seem to be a better predictor of the next days range?

Although I haven't done any statistical analysis on it. Larry Williams' book Long-Term Secrets to Short-Term Trading is one of many that have delved into this area.

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I tested those and both fall short compared to VIX.

For example, using the 3-day average -- I get only 68% of days that make this number the following day -- as compared to 82%+ for VIX. This is multiplying each by 0.8x (we want high odds of 'at least XX points' in range). Using things like the 3-day median or 10-day median yield similar results -- (each method calculated using the last 18 months as my test period).

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I misunderstood. I thought you were trying to predict range size and not whether the range size was "X" number of points or greater. Nevermind.

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stats are the same for either range or % of range....

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